Supermassive black holes are found in nearly all major galaxies and most are in a slowly accreting or quiescent state. The physical characteristics of these low-luminosity active galactic nuclei (LLAGN) allow a unique opportunity to build and test nearly \emph{ab initio} models of black hole accretion. To that end, I describe numerical techniques we have developed to build self-consistent dynamical and radiative models of LLAGN and their application to modeling the galactic center source Sgr A*.
Sgr A* is an extremely low luminosity LLAGN and is a particularly attractive target for modeling black hole accretion flows for a variety of reasons. First, its proximity has enabled excellent measurements of its mass and distance through long term monitoring of stellar orbits. Next, Sgr A* has been the target of extensive multiwavelength observing campaigns for decades, providing a wealth of information on its mean and fluctuating broadband spectrum. In the last few years, millimeter wavelength very long baseline interferometry has begun to resolve structure on the scale of the event horizon, providing constraints on the structure of the inner accretion flow. From a theoretical perspective, Sgr A* is an attractive target because its low luminosity implies that the dynamical and radiative problems are decoupled, greatly simplifying the construction of self-consistent models.
I first describe \grmonty, a fully relativistic Monte Carlo code for radiation transport that treats angle-dependent thermal synchrotron emission and absorption and Compton scattering essentially without approximation. One limitation of \grmonty\ is that it assumes the background emitting plasma (which is provided by, e.g., a simulation) is time-independent which we refer to as the ``fast-light'' approximation. I then describe the generalization of \grmonty\ to include light travel time effects in arbitrary time-dependent background flows and introduce a new technique for producing images based on time-dependent ray tracing.
Our aim was to model the time-dependent broadband spectrum of Sgr A* based on general relativistic magnetohydrodynamic (GRMHD) simulations. Before proceeding, we noted, as others have before us, that global disk simulations model transient accretion flows in the sense that the numerical values for, e.g., the density decay with time as the initial disk drains into the hole or exits the outer boundary. If left unaddressed, these transient models result in light curves that decay in time, in sharp contrast to the quasi-steady state that seems to pertain to systems like Sgr A*. To mitigate this problem, we derive and numerically solve the equations of one dimensional relativistic viscous disk evolution and use these results to motivate a smoothly varying time-dependent scaling between simulation and physical units. We show that this time-dependent scaling procedure effectively maps the transient GRMHD simulation data onto a quasi-steady solution that can then be used in radiative transfer calculations.
We then went on to modeling the time-dependent broadband spectrum of Sgr A* using GRMHD simulations, the time-dependent scaling described above, and the time-dependent extension of \grmonty. We found that our light curves are qualitatively similar to those observed. At near-infrared (NIR) and X-ray wavelengths, GRMHD models can produce modest flaring events broadly similar to flares observed from Sgr A*, though with some possible discrepancies. In particular, we find, in agreement with observations, 1) the NIR and X-ray flares are simultaneous, 2) they are $\sim 1\,{\rm hour}$ in duration, and 3) the NIR flare shows rich substructure while the X-ray flare is comparatively smooth.
Next, I describe our discovery of quasi-periodic structure in our simulated NIR and X-ray light curves of Sgr A*. We identify two peaks in the power spectral densities (PSDs) near the orbital frequency at the radius of the innermost stable circular orbit (ISCO). We attribute this quasi-periodicity to bright magnetic filaments dominated by $m=1$ azimuthal structure. The peak at higher frequency than the ISCO frequency is found to result from sub-ISCO emission. We argue that longer simulations would likely result in a single broad bump near the ISCO frequency rather than distinct peaks in the PSDs, but that excess power near the ISCO frequency is likely a robust result pertaining to hot, geometrically thick, optically thin disks.
Finally, I describe an ongoing effort to produce self-consistent models of LLAGN other than Sgr A*. Whereas in Sgr A* the dynamical and radiative problems are decoupled, other observable LLAGN have sufficient luminosity to make nonradiative GRMHD simulations inappropriate. Therefore I introduce \bhlight, a new numerical scheme for general relativistic radiation magnetohydrodynamics (GR-RMHD) based on the GRMHD code \harm\ and the relativistic Monte Carlo transport code \grmonty. \bhlight\ is fully conservative and formally applicable in all regimes of relativistic (and non-relativistic) radiation magnetohydrodynamics. In practice, shot noise from the Monte Carlo transport will likely limit its applicability to flows with low to moderate optical depths and our explicit integration scheme will only be efficient for relativistic flows. Fortunately, \bhlight\ should be well suited to studying the weakly radiative LLAGN. Though we plan to test \bhlight\ more extensively in the future, I present two test problems that demonstrate its functionality in limited regimes.